Opinion dynamics on tie-decay networks

TL;DR

This paper investigates how opinion dynamics evolve on tie-decay networks, where interactions influence tie strength that fluctuates over time, revealing insights into convergence speed and spectral properties in temporal social networks.

Contribution

It formulates continuous and discrete-time opinion models on tie-decay networks and analyzes spectral gaps, highlighting the effects of decay rates and interaction timing on convergence.

Findings

Empirical networks have smaller spectral gaps than randomized ones.

Spectral gap behavior is non-monotonic with respect to decay rate and time.

Slower decay rates can lead to faster convergence in opinion dynamics.

Abstract

In social networks, interaction patterns typically change over time. We study opinion dynamics on tie-decay networks in which tie strength increases instantaneously when there is an interaction and decays exponentially between interactions. Specifically, we formulate continuous-time Laplacian dynamics and a discrete-time DeGroot model of opinion dynamics on these tie-decay networks, and we carry out numerical computations for the continuous-time Laplacian dynamics. We examine the speed of convergence by studying the spectral gaps of combinatorial Laplacian matrices of tie-decay networks. First, we compare the spectral gaps of the Laplacian matrices of tie-decay networks that we construct from empirical data with the spectral gaps for corresponding randomized and aggregate networks. We find that the spectral gaps for the empirical networks tend to be smaller than those for the randomized and aggregate networks. Second, we study the spectral gap as a function of the tie-decay rate and time. Intuitively, we expect small tie-decay rates to lead to fast convergence because the influence of each interaction between two nodes lasts longer for smaller decay rates. Moreover, as time progresses and more interactions occur, we expect eventual convergence. However, we demonstrate that the spectral gap need not decrease monotonically with respect to the decay rate or increase monotonically with respect to time. Our results highlight the importance of the interplay between the times that edges strengthen and decay in temporal networks.